Question

write and solve an equation that represents the following math sentence. twenty - nine equals the sum of 11.5 and the quotient of a number and 2.5. \\(\bigcirc\\ 29 = 11.5+\frac{m}{2.5};m = 43.75\\) \\(\bigcirc\\ 29 = 11.5+\frac{m}{2.5};m = 7\\) \\(\bigcirc\\ 29 = 11.5 + 2.5m;m = 43.75\\) \\(\bigcirc\\ 29 = 11.5 + 2.5m;m = 7\\)

Explanation:

Step1: Analyze the equation structure

The math sentence says "Twenty - nine equals the sum of 11.5 and the quotient of a number and 2.5". Let the number be \(m\). The quotient of \(m\) and 2.5 is \(\frac{m}{2.5}\), and the sum of 11.5 and this quotient is \(11.5+\frac{m}{2.5}\). So the equation is \(29 = 11.5+\frac{m}{2.5}\).

Step2: Solve the equation for \(m\)

Subtract 11.5 from both sides of the equation \(29=11.5 + \frac{m}{2.5}\):
\(29-11.5=11.5+\frac{m}{2.5}-11.5\)
\(17.5=\frac{m}{2.5}\)
Multiply both sides by 2.5 to solve for \(m\):
\(m = 17.5\times2.5\)
\(m=43.75\)

Wait, but there is a contradiction with the marked option. Let's re - check the equation construction. The problem says "the sum of 11.5 and the quotient of a number and 2.5". The quotient of a number (\(m\)) and 2.5 is \(\frac{m}{2.5}\), so the equation is \(29=11.5+\frac{m}{2.5}\). Solving it:

\(29 - 11.5=\frac{m}{2.5}\)

\(17.5=\frac{m}{2.5}\)

\(m=17.5\times2.5 = 43.75\)

So the correct equation is \(29 = 11.5+\frac{m}{2.5}\) and \(m = 43.75\), which is the first option.

Answer:

A. \(29 = 11.5+\frac{m}{2.5};m = 43.75\)